arXiv:hep-ph/0504199v1 21 Apr 2005 siaeo h H xetto 3.Teitrs fsc vnsi r is events such of interest The c t [3]. The diffractive expectation [2]. central LHC the the in at of expected observed estimate been be effectively to has is production mode production This oo n o ur asmaueeta rdcinthreshold production at measurement mass pa the o objects. study top examples heavy or and As mass, boson distributions. particle’s W angular heavy and I the cross-sections studied. extract accurately measuring be to can attempt process p hard and the the to of access dynamics gives the measurement and proton the protons, outgoing fe ev h neato einitc,adcnb esrdusin measured object be heavy can the and events, intact, of region category interaction the this leave In often LHC. the at (DPE), hsscin W section. this asmaueet.W hncnld ntemto ngnrl on applications. general, further in of method pa the number on following a fits conclude mention The “histogram” then We (“turn-on”and analysis. version measurements. the twofold mass in a used in cuts method, scan the and effects, detector t of and sbsclyn netit ocrigtepsiiiyo esrn the fr measuring suffer exchange, of possibility double exclusive the in concerning produced uncertainty events, no basically is ∗ † ‡ ¶ § lcrncaddress: Electronic lcrncaddress: Electronic lcrncaddress: Electronic lcrncaddress: Electronic R 36 nted ehrh soie uCNRS. associ´ee au recherche unit´e de 2306, URA eas consider also We epooeanwmto omauehaypril rprisvad via properties particle heavy measure to method new a propose We fteeet are events the If arpouto fWbsn n o ursi E n obepomero double and QED in top and bosons W of production Pair h ae sognsda olw.W tr ygvn h theoretical the giving by start We follows. as organised is paper The evc epyiu e atcls E/aly 19 Gif- 91191 CEA/Saclay, particules, des physique de Service ¯ rdcin(nbt xlsv n nlsv P) ete eciet describe then We DPE). inclusive and exclusive both (in production t rtduigteeape fteWbsnadtpqakms mea mass quark top and boson W the mentioned. of centra are examples in the curves using excitation trated exploits method The detectors. epooeanwsto esrmnswihcnb efre at performed be can which measurements of set new a propose We + W [email protected] [email protected] [email protected] [email protected] evc epyiu e atcls E/aly 19 Gif- 91191 CEA/Saclay, particules, des physique de Service inclusive exclusive − evc epyiu herqe E/aly 19 Gif-sur 91191 th´eorique, CEA/Saclay, physique de Service ar r rdcdi htnmdae rcse,wihaeexac are which processes, photon-mediated in produced are pairs hehl cn nCnrlDffato tteLHC the at Diffraction Central in scans Threshold obepmrnexchange, pomeron double , i.e. fn te atce r rdcdi diint h aro ev ob heavy of pair the to addition in produced are particles other no if , I HOEIA FORMULATION THEORETICAL II. nvriyo ohse,NwYr,USA York, New Rochester, of University .INTRODUCTION I. .Boonekamp M. .Peschanski R. .Cammin J. .Royon C. i.e. vnsweeohrprilsacmaytehaysystem. heavy the accompany particles other where events , u-vtecdx rne n emlb aai,USA Batavia, Fermilab, and France, cedex, sur-Yvette ¶ oo-htno oeo-oeo eteo-as[1], centre-of-mass pomeron-pomeron or hoton-photon mtertclucranissneecuiediffractive exclusive since uncertainties theoretical om † ¯ rdcin ic nlsv obedffatv dijet diffractive double inclusive since production, t atclr n a bev h hehl excitation threshold the observe can one particular, n r rdcdi ar,weesteba particles beam the whereas pairs, in produced are s ,adisapiaint h oo n o quark top and boson W the to application its and ), ‡ ∗ irciepi rdcin n sillus- is and production, pair diffractive l hsapoc,w ieadtie con fthe of account detailed a give we approach, this f eyfraddetectors. forward very g osscinmaueeto 2 losfrarough a for allows [2] of measurement ross-section tces(osbyeeg-eedn)culnsby couplings energy-dependent) (possibly rticle’s eviewed. to h ae ecie ndti h threshold the detail in describes paper the of rt h bv asmaueet npriua,and particular, in measurements mass above the h ehdcnesl eetne oother to extended be easily can method The . epoessa h H.O h otay t contrary, the On LHC. the at processes se omlto fW of formulation ul htnaddul oeo exchange pomeron double and photon ouble ueet.Frhrapplications Further surements. u-vtecdx France cedex, sur-Yvette Yet ee,France cedex, -Yvette xhneaedsrbdi ealin detail in described are exchange n eeetgnrto,tesmlto of simulation the generation, event he h H sn oa pot roman using LHC the l aclbei E.There QED. in calculable tly + W − rdcin(i QED) (via production § et n the and jects ¯ t 2 production is still to be observed at the Tevatron, and other models lead to different cross sections, and thus to a different potential for the top quark mass measurement. However, since the exclusive kinematics are simple, the model dependence will be essentially reflected by a factor in the effective luminosity for such events. By contrast, the existence of inclusive double pomeron exchange — in other words, when the pomeron remnants carry a part of the available center-of-mass energy — is certain since it has been observed already in experiments. We will mention at the end how these events could be used and the interest of their experimental determination. We will briefly analyse their impact on the t¯t threshold scan but we postpone a precise study of such events to a forthcoming publication. p p Pom

γ 1 g W W g t t g γ

Pom

p p

FIG. 1: W+W− (QED) and t¯t (QCD) exclusive production. Left: double photon exchange process. Right: exclusive double pomeron exchange in the Bialas-Landshoff model via “gluons in the pomeron”; The grey band represents the rapidity gap survival suppression factor (see text).

A. W+W− production via double photon exchange

The QED process rates are obtained from the following cross section formula

γ γ − − dσ(pp→ p W+W p) =σ ˆγγ→W+W dn1 dn2 , where the Born γγ W+W− cross-section reads [4] → 2 8πα 1 3 2 1+Λ σˆ + − = 1+ t +3t Λ 3t(1 2t) ln , (1) γγ→W W M 2  t  4  − −  1 Λ WW − with m2 W √ t = 2 , Λ= 1 4t , (2) MWW −

+ − γ where MWW is the total W W mass. The photon fluxes dn are given by [5]

2 2 γ α ω ω qmax qmin dn = 1 φ 2 φ 2 , (3) π ω  − E    q0  −  q0  where x 1 (1 b)y 2+2x b bk φ (x) (1+ay) ln +Σ3 ln +Σ3 , (4) k=1 k 3− 1 − k=1 k ≡  1+ x k(1 + x) − 4x(1 + x) + c(1 + 4 y)   1+ x  k(1 + x)  and ω2 q2 0.71 GeV2 ; y = ; a 7.16 ; b 3.96 ; c 0.028 , (5) 0 ∼ E(E ω) ∼ ∼− ∼ − 3 in the usual dipole approximation for the proton electromagnetic form factors. ω is the photon energy in the laboratory frame, q2 the modulus of its mass squared in the range

m2ω2 t q2 , q2 , max , (6) min max ≡ E(E ω) q2    − 0 2 2 where E and m are the energy and mass of the incident particle and tmax (mW/MWW)max is defined by the experimental conditions. ≡ The QED cross section dσ(pp p W+W−p) is a theoretically clear prediction. One should take into account however, two sources of (probably→ mild) correction factors. One is due to the soft QCD initial state radiation between incident protons which could destroy the large rapidity gap of the QED process. It is present but much less pronounced than for the rapidity gap survival for a QCD hard process (see the discussion in the next subsections), thanks to the large impact parameter implied by the QED scattering. The second factor is the QCD gg W+W− exclusive production via higher order diagrams. This has been evaluated recently [6] for standard (non diffractive)→ production to give a 5% correction factor. The similar calculation for the diffractive W+W− production by comparison with the QED process is outside the scope of our paper but deserves to be studied together with the “inclusive” background (W+W−+hadrons) it could generate.

B. Exclusive diffractive production of t¯t events

Let us introduce the model [7, 8] we shall use for describing exclusive t¯t production in double diffractive production. This process is depicted in Fig. 1 (right). In [7], the diffractive mechanism is based on two-gluon exchange between the two incoming protons. The soft pomeron is seen as a pair of gluons non-perturbatively coupled to the proton. One of the gluons is then coupled perturbatively to the hard process (either the Higgs boson, or the t¯t pair, see Fig. 1), while the other one plays the rˆole of a soft screening of colour, allowing for diffraction to occur. The corresponding cross-sections for q¯qand Higgs boson production read:

2ǫ ′ 2 exc exc s (2) 2 2 2α vi 2 dσ ¯ (s)= C δ  (vi + ki) d vid kidηi ξ exp( 2λ ¯v )σ ˆ ¯ , (7) tt q¯q M 2  i − tt i tt q¯q iX=1,2 i=1Y,2   where the variables vi and ki respectively denote the transverse momenta of the outgoing protons and of top quarks, ξi are the proton fractional momentum losses, and ηi are the quark rapidities,

2 π dσ ρ(1 ρ) 4mt σˆt¯t = 2 − 2 , ρ = 2 (8) ≡ 24 dt mT 1mT 2 Mt¯t is the hard gg t¯t cross-section. In the model,→ the soft pomeron trajectory is taken from the standard Donnachie-Landshoff parametrisation [9], ′ ′ −2 exc namely α(t)=1+ ǫ + α t, with ǫ 0.08 and α 0.25GeV . λt¯t and the normalization Ct¯t are kept as in the original paper [7]. Note that, in this≈ model, the strong≈ (non perturbative) coupling constant is fixed to a reference value G2/4π =1, reflecting the lack of knowledge of the absolute normalization of exclusive DPE processes.

C. Inclusive diffractive production of t¯t events

It is convenient to introduce also the model for central inclusive diffractive production [3] applied to t¯t dijets. One writes

g g 2ǫ ′ 2 incl x1x2s (2) g 2 2 2α vi 2 g g dσ ¯ = C ¯ δ  vi +ki dξidx d vid kiξi exp 2v λ ¯ σ ¯ GP (x ,µ)GP (x ,µ) . (9) tt tt  M 2  i − i tt tt 1 2 t¯t iX=1,2 i=1Y,2n o   g In the above, xi are the pomeron’s momentum fractions carried by the gluons or quarks involved in the hard pro- g cess, and the GP is the gluon energy density in the pomeron, i.e., the gluon density multiplied by xi . We use as parameterisations of the pomeron structure functions the fits to the diffractive HERA data performed in [10]. The 4 normalization Ct¯t is obtained from the description [3] of the jet-jet diffractive cross-section at the Tevatron [2]. The hard cross-section σt¯t to be considered is now ρ ρ 9ρ σt¯t = t 2 t 2 1 1 , (10) (mT 1) (mT 2)  − 2  − 16 to be distinguished fromσ ˆt¯t (8) due to inclusive characteristics [3].

D. Rapidity Gap Survival

In order to select exclusive diffractive states, such as for W+W− (QED) and t¯t (exclusive, QCD), it is required to take into account the corrections from soft hadronic scattering. Indeed, the soft scattering between incident particles tends to mask the genuine hard diffractive interactions at hadronic . The formulation of this correction [11] to the scattering amplitude ¯ consists in considering a gap survival probability (SP ) function S such that A(WW,tt)

2 (pT 1,pT 2, ∆Φ) = 1+ SP , ¯ , ¯ = d kT (kT ) , ¯ (pT 1 kT , pT 2 +kT ) , (11) A { A } ×A(WW tt) ≡ S×A(WW tt) Z S A(WW tt) − where pT 1,2 are the transverse momenta of the outgoing p, p¯ and ∆Φ their azimuthal angle separation. SP is the soft scattering amplitude. A The correction for the QED process is present but much less pronounced than for the rapidity gap survival for a QCD hard process, thanks to the large impact parameter implied by the QED scattering. In a specific model [12] the correction factor has been evaluated to be of order 0.9 at the LHC for γγ H. It is evaluated to be of order 0.03 for the QCD exclusive diffractive processes at the LHC. →

III. EXPERIMENTAL CONTEXT

A. The DPEMC Monte Carlo

A recently developed Monte-Carlo program, DPEMC [13], provides an implementation of the W+W− and t¯t events described above in the QED and both exclusive and inclusive double pomeron exchange modes. It uses HERWIG [14] as a cross-section library of hard QCD processes, and when required, convolutes them with the relevant pomeron fluxes and parton densities. The survival probabilities discussed in the previous section (respectively 0.9 for double photon and 0.03 for double pomeron exchange processes) have been introduced at the generator level. The cross section at the generator level for W+W− QED and exclusive diffractive t¯t production is found to be 55.9 fb and 40.1 fb for a mW mass of 80.42 GeV and a top mass of 174.3 GeV after applying the survival probabilities.

B. Roman pot detector positions and resolutions

A possible experimental setup for forward proton detection is described in detail in [15]. We will only describe its main features here and discuss its relevance for the W boson and top quark masses measurements. In exclusive DPE or QED processes, the mass of the central heavy object can be reconstructed using the roman 2 pot detectors and tagging both protons in the final state at the LHC. It is given by M = ξ1ξ2s, where ξi are the proton fractional momentum losses, and s the total center-of-mass energy squared. In order to reconstruct objects with masses in the 160 GeV range (for W+W− events) in this way, the acceptance should be large down to ξ values as low as a few 10−3. For t¯t events, an acceptance down to 10−2 is needed. The missing mass resolution directly depends on the resolution on ξ, and should not exceed a few percent to obtain a good mass resolution. These goals can be achieved if one assumes two detector stations, located at 210 m, and 420 m [15] from the interaction point1. The ξ acceptance and resolution have been derived for each device∼ using a complete∼ simulation of the LHC beam parameters. The combined ξ acceptance is close to 60% at low masses (at about twice m ), and ∼ W

1 A third position at 308 m is often considered as well but is more difficult from a technological point of view at the LHC and was not considered for this study. 5

90% at higher masses starting at about 220 GeV. for ξ ranging from 0.002 to 0.1. The acceptance limit of the device closest to the interaction point is ξ > ξmin =0.02. Let us note also that the acceptance for t¯t events goes down to 20% if only roman pots at 210 m are present since most of the events are asymmetric (one tag at 420m and another one at 210m). Our analysis does not assume any particular value for the ξ resolution. We will discuss in the following how the resolution on the W boson or the top quark masses depend on the detector resolutions, or in other words, the missing mass resolution.

C. Experimental cuts

This section summarises the cuts applied in the remaining part of the analysis. As said before, both diffracted protons are required to be detected in roman pot detectors. The triggers which will be used for the W+W− and t¯t events will be the usual ones at the LHC requiring in addition a positive tagging in the roman pot detectors. The experimental offline cuts and their efficiencies have been obtained using a fast simulation of the CMS detector [16] as an example, the fast simulation of the ATLAS detector leading to the same results. If we require at least one lepton (electron or muon) with a transverse momentum greater than 20 GeV and one (two) jet with a transverse momentum greater than 20 GeV (40 GeV) for W+W− (t¯t) to be reconstructed in the acceptance of the main detector in addition to the tagged protons 2, we get an efficiency of about 50% for t¯t events, and 30% for W+W− events. We give the mass resolution as a function of luminosity in the following after taking into account these efficiencies. If the efficiencies are found to be higher, the luminosities have to be rescaled by this amount.

IV. THRESHOLD SCAN METHODS

A. Explanation of the methods

We study two different methods to reconstruct the mass of heavy objects double diffractively produced at the LHC. As we mentioned before, the method is based on a fit to the turn-on point of the missing mass distribution at threshold. One proposed method (the “histogram” method) corresponds to the comparison of the mass distribution in data with some reference distributions following a Monte Carlo simulation of the detector with different input masses corresponding to the data luminosity. As an example, we can produce a data sample for 100 fb−1 with a top mass of 174 GeV, and a few MC samples corresponding to top masses between 150 and 200 GeV by steps of. For each Monte Carlo sample, a χ2 value corresponding to the population difference in each bin between data and MC is computed. The mass point where the χ2 is minimum corresponds to the mass of the produced object in data. This method has the advantage of being easy but requires a good simulation of the detector. The other proposed method (the “turn-on fit” method) is less sensitive to the MC simulation of the detectors. As mentioned earlier, the threshold scan is directly sensitive to the mass of the diffractively produced object (in the W+W− case for instance, it is sensitive to twice the W mass). The idea is thus to fit the turn-on point of the missing mass distribution which leads directly to the mass of the produced object, the W boson. Due to its robustness, this method is considered as the “default” one in the following. To illustrate the principle of these methods and their achievements, we apply them to the W boson and the top quark mass measurements in the following, and present in detail the reaches at the LHC. They can be applied to other threshold scans as well.

B. W mass measurement

In this section, we will first describe the result of the “turn-on fit” method to measure the W mass. As we mentioned earlier, the advantage of the W+W− processes is that they do not suffer from any theoretical uncertainties since this

2 The double pomeron exchange background to the signal is found to be small, and will more correspond to misidentifications of jets as leptons in the main detector. Since this is difficult to evaluate precisely using a fast simulation of the detector, and this is quite small compared to the signal, we decided not to incorporate it in the following study. 6

9 9

8 8 Events Events

7 7

6 6

5 5

4 4

3 3

2 2

1 1

0 0 140 150 160 170 180 190 200 210 220 140 150 160 170 180 190 200 210 220 total pot mass (GeV) total pot mass (GeV)

FIG. 2: Two examples of fits to missing mass reference distributions with a resolution of the roman pot detectors of 1 GeV (left) and 3 GeV (right). We see on these plots the principle and the accuracy of the “turn-on fits” to the MC at threshold.

10 10

8 8 Resolution of roman pots: 1.0 GeV Resolution of roman pots: 3.0 GeV 6 6

- 80.42 GeV 4 - 80.42 GeV 4 fit fit

m 2 m 2

0 0

-2 -2

-4 -4 y = p + p x y = p + p x 0 1 0 1 -6 -6 p = -87.260 +/- 3.483 p = -73.414 +/- 0.793 0 0 -8 -8 p = 1.096 +/- 0.043 p = 0.934 +/- 0.010 1 1 -10 -10 76 78 80 82 84 76 78 80 82 84 mW (GeV) mW (GeV)

FIG. 3: Calibration curves (see text) for two different roman pot resolutions of 1 GeV (left) and 3 GeV (right). We notice that the calibration can be fitted to a linear function with good accuracy. The dashed line indicates the first diagonal to show the shift clearly. is a QED process. The W mass can be extracted by fitting a 4-parameter ‘turn-on’ curve to the threshold of the mass distribution (c.f. Ref. [17]):

x−P2 −1 − P = P1 e 3 +1 + P4 . (12) F · h i 

P1 is the amplitude, P2 the inflexion point, P3 the width of the turn-on curve, and P4 is a vertical offset, x being the missing mass. With a detector of perfect resolution, P2 would be equal to twice the W mass. However, the finite roman pot resolution leads to a shift between P2 and 2mW which has to be established using a MC simulation of the detector for different values of its resolution. This shift is only related to the method itself and does not correspond to any error in data. For each value of the W input mass in MC, one has to obtain the shift between the reconstructed mass (P2/2) and the input mass, which we call in the following the calibration curve. It is assumed for simplicity that P2 is a linear function of mW, which is a good approximation as we will see next. In order to determine the linear dependence between P2 and mW, calibration curves are calculated for several assumed resolutions of the roman pot detectors. The calibration points are obtained by fitting to the mass distribution of high statistics samples (100 000 F events) for several values of mW. An example is given in Fig. 2 for two resolutions of the roman pot detectors. The difference between the fitted values of P2/2 and the input W masses are plotted as a function of the input W mass and are then fitted with a linear function. To minimise the errors on the slope and offset, the difference P /2 80.42 GeV 2 − is plotted versus mW (Fig. 3). To evaluate the statistical uncertainty due to the method itself, we perform the fits with some 100 different “data” ensembles. For each ensemble, one obtains a different reconstructed W mass, the dispersion corresponding only to statistical effects. The expected statistical uncertainty on the actual measurement of the W mass in data is thus estimated with these ensemble tests for several integrated luminosities and roman pot resolutions. Each ensemble contains a number of events that corresponds to the expected event yield for a given integrated luminosity, taking into account selection and acceptance efficiencies. The turn-on function is fitted to each ensemble. Only the parameters F 7

70 70

60 Entries Entries 60

50 50

40 40

30 30

20 20

10 10

0 0 76 77 78 79 80 81 82 83 84 85 76 77 78 79 80 81 82 83 84 85 Fitted W mass (GeV) Fitted W mass (GeV)

FIG. 4: Distribution of the fitted value of the W mass from ensemble tests. Left: corresponding to 150 fb−1, right: corresponding to 300 fb−1. We note the resolution obtained on the W mass for these two luminosities.

1.4 res = 3.0 GeV (GeV)

W 1.2 res = 2.0 GeV res = 1.0 GeV 1

0.8

0.6

0.4

0.2 Expected stat. uncertainty m

0 100 200 300 400 500 600 Integrated luminosity (fb-1)

FIG. 5: Expected statistical uncertainty on the W mass as a function of luminosity for three different roman pot resolutions.

P1 and P2 are allowed to float, P3 and P4 are fixed to the average values obtained from the fits for the calibration points. fit In order to obtain the fitted estimate for the W mass, mW, in each ensemble, the fit value of P2 is corrected with the fit calibration curve that corresponds to the roman pot resolution. For each resolution mW is histogrammed as shown in Fig. 4. The distributions are fitted with a Gauss function where the width corresponds to the expected statistical uncertainty of the W mass measurement. Fig. 5 shows the expected precision as a function of the integrated luminosity −1 for several roman pot resolutions. With 150 fb the expected statistical uncertainty on mW is about 0.65 GeV when −1 a resolution of the roman pot detectors of 1 GeV can be reached. With 300 fb the expected uncertainty on mW decreases to about 0.3 GeV. We notice of course that this method is not competitive to get a precise measurement of the W mass, which would require a resolution to be better than 30 MeV. However, this method can be used to align precisely the roman pot detectors for further measurements. A precision of 1 GeV (0.3 GeV) on the W mass leads directly to a relative resolution of 1.2% (0.4%) on ξ using the missing mass method. This calibration will be needed, for instance, to measure the top mass as proposed in the next section. Let us now present the result on the “histogram” method, which is an alternative approach to determine the W mass. The same high statistics templates used to derive the calibration curves are fitted directly to each ensemble (see Fig. 6 left). The χ2 is defined using the approximation of poissonian errors as given in Ref. [18]. Each ensemble thus gives a χ2 curve which in the region of the minimum is fitted with a fourth-order polynomial (Fig. 6 right). The min position of the minimum of the polynomial, mW , gives the best value of the W mass and the uncertainty σ(mW) is 2 2 obtained from the values where χ = χmin +1. The mean value of σ(mW) for all ensembles are quoted as expected statistical uncertainties. The expected statistical errors on the W mass using histogram fitting are comparable to those using the function fitting method. However, the former turns out to be more sensitive to the resolution of the roman pot detectors.

C. Top mass measurement

The method to extract the top mass is the same as for the W mass described in the previous section. The theoretical cross section is not as well known as for the W and is model dependent. Our study assumes the Bialas Landshoff model for exclusive t¯t production. For t¯t events the width of the turn-on curve is considerably larger than for WW 8

2 180 χ 60 160 Events

50 140

120 40 100 30 80 20 60

10 40

0 20 140 150 160 170 180 190 200 210 220 76 78 80 82 84 86 total pot mass(GeV) mW (GeV)

FIG. 6: Left: Example of the histogram-fitting method. We see the difference between the “data” sample (full histogram 2 with error bars, mW = 80.42 GeV) and a reference histogram (dashed line, mW = 85.42 GeV). Right: Example of the χ distribution in one ensemble.

1

0.9 res = 3.0 GeV (GeV)

W 0.8 res = 2.0 GeV res = 1.0 GeV 0.7

0.6

0.5

0.4

0.3

0.2

Expected stat. uncertainty m 0.1

0 100 200 300 400 500 600 Integrated luminosity (fb-1)

FIG. 7: Expected statistical precision of the W mass as a function of the integrated luminosity for various resolutions of the roman pot detectors using the histogram-fitting method. events (Fig. 8, left), resulting in a larger offset between the actual turn on and the inflexion point of the fit function3. The calibration curve for a resolution of the roman pot detectors of 1 GeV is displayed in Fig. 8, right. Ensemble tests for integrated luminosities of 50, 75, 100 and 200 fb−1 and roman pot detector resolutions of 1 GeV, 2 GeV and 3 GeV yield the results shown in Fig. 9, left. Resolutions of the roman pot detectors between 1 GeV and 3 GeV give similar statistical uncertainties on the top quark mass which is due to the fact that the main limiting effect on resolution is statistics. With 100 fb−1 the expected statistical precision is about 1.6 GeV and gets improved to about 0.65 GeV with 300 fb−1. The results have also been cross-checked using the histogram fitting method which was found to yield very similar expected uncertainties as the function fitting method (Fig. 9, right).

V. OUTLOOK AND PROSPECTS

In this section, we discuss other applications of the threshold scan method. Detailed analysis is postponed to forthcoming papers [19]. As we mentioned before, the cross section of exclusive top pair production at the LHC is still uncertain, and predictions will be constrained by the incoming results form the Tevatron, especially from the DØ experiment where it is possible to detect double tagged events. On the contrary, inclusive double pomeron exchange has already been observed, and top quark pair production in this mode is fairly certain at the LHC. In this case, the threshold excitation is sensitive to quark and gluon densities at high pomeron momentum fraction, so that these events provide a rather unique opportunity to study structure functions near the endpoint.

3 Note in addition that the top quark width is not included in Herwig and thus in our study. However, this effect is expected to be small. 9

30 12 25 Resolution of roman pots: 1.0 GeV Events 10 20 - 175 GeV fit

8 m 15

10 6 5

4 0 y = p + p x -5 0 1 2 p = -162.707 +/- 4.868 0 -10 p = 0.989 +/- 0.028 1 0 -15 300 320 340 360 380 400 420 440 460 480 500 165 170 175 180 185 total pot mass (GeV) mtop (GeV)

FIG. 8: Fit to a reference mass distribution with mt = 175 GeV (left) and calibration curve for a roman pot resolution of 1 GeV, the diagonal is displayed in dashed line to show the difference (right). Note the larger difference between the calibration curve and the diagonal compared to the case of W+W− production.

2.4 2.4

2.2 res = 3.0 GeV 2.2 res = 3.0 GeV (GeV) (GeV) t res = 2.0 GeV t res = 2.0 GeV 2 2 res = 1.0 GeV res = 1.0 GeV 1.8 1.8

1.6 1.6

1.4 1.4

1.2 1.2

1 1

0.8 0.8 Expected stat. uncertainty m Expected stat. uncertainty m

0.6 0.6 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 -1 Integrated luminosity (fb-1) Integrated luminosity (fb )

FIG. 9: Expected statistical precision of the top mass as a function of the integrated luminosity for various resolutions of the roman pot detectors (full line: resolution of 1 GeV, dashed line: 2 GeV, dotted line: 3 GeV). Left: function fitting method, right: histogram fitting method (the three curves for different roman pot resolutions lead to the same results and cannot be distinguished in the figure).

To illustrate this point, we give in Fig. 10 the missing mass distributions at the generator level using the DPEMC Monte Carlo for the exclusive t¯t events (full line) and the results on the Bialas-Landshoff inclusive t¯t production for two different gluon densities in the pomeron (dashed line: fit 1, dotted line: fit 2, see Ref. [20]). Fit 2 in Ref [20] leads to a more prominent gluon at high β than fit 1. We see that the missing mass distribution is directly sensitive to the parton distributions in the pomeron. In Fig. 11, we display the differences between the exclusive t¯t events in full line and the result of the factorisable POMWIG model (dotted line), and the non factorisable one based on the Bialas-Landshoff approach. We see again that the missing mass distribution, and thus the threshold analysis can help distinguishing between the models. Another application of exclusive pair-production consists in measuring the mass of stops and sbottoms, provided these particles exist and can be produced in pairs at the LHC. Finally, W pair-production in central diffraction gives access to the couplings of gauge bosons. Namely, as we mentioned already, W+W− production in two-photon exchange is robustly predicted within the . Any anomalous coupling between the photon and the W will reveal itself in a modification of the production cross section, or by different angular distributions. Since the cross-section of this process is proportional to the fourth power of photon-W coupling, good sensitivity is expected.

VI. CONCLUSION

Recent work on DPE has essentially focused on the Higgs boson search in the exclusive channel. In view of the difficulties and uncertainties affecting this search [8], we highlight new aspects of double diffraction which complement the diffractive program at the LHC. 10

3500

3000

2500

2000

1500

1000

500

0 400 600 800 1000 1200 1400 Central mass (GeV)

FIG. 10: Missing mass distributions at the generator level using the DPEMC Monte Carlo for the exclusive t¯t events in full line and the results on inclusive t¯t production for two different gluon densities in the pomeron (dashed line: fit 1, dotted line: fit 2, see Ref. [20]).

3500

3000

2500

2000

1500

1000

500

0 400 600 800 1000 1200 1400 Central mass (GeV)

FIG. 11: Missing mass distributions at the generator level using the DPEMC Monte Carlo for the exclusive t¯t events in full line, the inclusive events from model [3, 8] (dashed line), and [21] (dotted line), see text.

In particular, QED W pair production provides a certain source of interesting diffractive events. Inclusive t¯t production via double pomeron exchange is also an open channel and will provide interesting information on a poorly known aspect of structure functions. These robust channels will help and accompany the understanding of the more intriguing and challenging problem of exclusive double diffraction. In this paper, we have advocated the interest of threshold scans in double pomeron exchange. This method considerably extends the physics program at the LHC. To illustrate its possibilities, we described in detail the W boson and the top quark mass measurements. The precision of the W mass measurement is not competitive with other methods, but provides a very precise calibration of the roman pot detectors. The precision of the top mass measurement is however competitive, with an expected precision better than 1 GeV at high luminosity. Other 11 promising applications remain to be investigated.

[1] M. G. Albrow and A. Rostovtsev [arXiv:hep-ph/0009336]. [2] T. Affolder et al. [CDF Collaboration], Phys. Rev. Lett. 85, 4215 (2000). [3] M. Boonekamp, R. Peschanski and C. Royon, Phys. Rev. Lett. 87, 251806 (2001) [arXiv:hep-ph/0107113]. [4] E. Papageorgiu, Phys. Lett. B 250, 155 (1990). [5] V. M. Budnev, A. N. Vall and V. V. Serebryakov, Yad. Fiz. 21, 1033 (1975). [6] T. Binoth, M. Ciccolini, N. Kauer and M. Kramer, arXiv:hep-ph/0503094. [7] A. Bialas and W. Szeremeta, Phys. Lett. B296 (1992) 191; A. Bialas and R. Janik, Zeit. f¨ur. Phys. C62 (1994) 487. [8] M. Boonekamp, R. Peschanski and C. Royon, Nucl. Phys. B 669, 277 (2003) [Erratum-ibid. B 676, 493 (2004)] [arXiv:hep- ph/0301244]; Phys. Lett. B 598, 243 (2004) [arXiv:hep-ph/0406061]. [9] A. Donnachie, P. V. Landshoff, Phys. Lett. B207 (1988) 319. [10] C. Royon, L. Schoeffel, J. Bartels, H. Jung, R. Peschanski, Phys. Rev. D63 (2001) 074004. [11] J. D. Bjorken, Phys. Rev. D47, (1993) 101; E. Gotsman, E. Levin and U. Maor, Phys. Lett. B438 (1998), 229; A. B. Kaidalov, V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C21 (2001) 521. [12] V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C 23, 311 (2002) [arXiv:hep-ph/0111078]. [13] M. Boonekamp, T. Kucs, Comput. Phys. Commun. 167 (2005) 217. [14] G. Corcella et al., JHEP 0101:010 (2001). [15] J. Kalliopuska, T. M¨aki, N. Marola, R. Orava, K. Osterberg,¨ M. Ottela, HIP-2003-11/EXP. [16] CMSIM, fast simulation of the CMS detector, CMS Collab., Technical Design Report (1997); TOTEM Collab., Technical Design Report, CERN/LHCC/99-7; ATLFAST, fast simulation of the ATLAS detector, ATLAS Collab, Technical Design Report, CERN/LHC C/99-14. [17] G. Abbiendi et al. [OPAL Collaboration], Eur. Phys. J. C 26, 321 (2003) [arXiv:hep-ex/0203026]. [18] N. Gehrels, Astrophys. J. 303, 336 (1986). [19] M. Boonekamp, J. Cammin, S. Lavignac, R. Peschanski, C. Royon, in preparation. [20] C. Royon, L. Schoeffel, J. Bartels, H. Jung, R. Peschanski, Phys.Rev. D63 (2001) 074004, a fit to the data from H1 Coll., Z. Phys. C76 (1997) 613. . [21] B. E. Cox and J. R. Forshaw, Comput. Phys. Commun. 144, 104 (2002) [arXiv:hep-ph/0010303].